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Isospectral sets for akns systems on the unit interval with generalized periodic boundary conditions

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Abstract

We analyze isospectral sets of potentials associated with generalized periodic boundary conditionsB inSL (2, ℝ) for the 2 ×2AKNS systems on the unit interval. WhenB is a rotation we get the usual periodic case. WhenB is not a rotation isospectral sets are cylindrical real analytic submanifolds ofL 2ℝ ([0, 1])2 ×SL(2, ℝ) and their sections for fixed boundary conditions are real analytic submanifolds ofL 2ℝ ([0, 1])2.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, U.R.A. C.N.R.S. 1870 Université de Reims Moulin de la Housse, BP 1039, 51687, Reims Cedex 2, France

    L. Amour

  2. Département de Mathématiques, U.R.A. C.N.R.S. 742 Institut Galilée, Université Paris-Nord, 93430, Villetaneuse, France

    J. C. Guillot

  3. CMAP, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    J. C. Guillot

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  1. L. Amour
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  2. J. C. Guillot
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Amour, L., Guillot, J.C. Isospectral sets for akns systems on the unit interval with generalized periodic boundary conditions. Geometric and Functional Analysis 6, 1–27 (1996). https://doi.org/10.1007/BF02246765

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  • DOI: https://doi.org/10.1007/BF02246765

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